Mathematica: Matrices

1. Comments!!! Be sure to use comments on all of your as signments to make them
easier to understand.

2. Vectors: To define a vector enter it in Mathematica as :
v = {a, b, c}

a. Enter the vector 4i + 5j -2k for the variable v
b . Enter the vector -8i -3j +5k for the variable w

*Note: if you just want a vector with integers use the Range [first #, last #, step]

c. Create a vector using the range command that goes from 0 to 1 with a step size
of .2
d. Create a vector that starts at x and ends at x + 5

3. Dot and Cross Product:
A) Dot product: Dot[v₁,v₂] where v₁ and v₂ are two vectors

a. Take the dot product of the two vectors that you defined earlier
b. Does the answer make sense?

B) Cross product: Cross[v₁,v₂] where v₁ and v₂ are two vectors

a. Take the cross product of the two vectors that you defined earlier
b. Does your answer make sense?

4. Matrices: In Mathematica matrices are defined as lists. To define the matrix
do so in the fol lowing way : {{a, b, c, d}, {e, f, g ,h}, {i, j, k, l}, {m, n, o, p}}

a. Enter the matrix as m in Mathematica
b. Enter the matrix  as p in Mathematica

*You will note that when you enter a matrix everything is on the same line . To
make the matrix with the numbers in rows and columns use the MatrixForm command.

c. Use the command MatrixForm on the two matrices from parts a and b.

5. Identity Matrix: The identity matrix, which is defined in Mathematica, is always a
square matrix . To get an identity matrix enter Identity Matrix[# of rows].

a. Create an identity matrix with 4 rows and 4 columns
b. Create an identity matrix with 5 rows and 5 columns
c. Do you understand what an identity matrix looks like ?

6. Transposing a Matrix: To transpose a matrix (put what was the first row as the
first column, the second row as the second column, etc.) use the Transpose [matrix]

a. Transpose the matrix (1,2,3,4,5)
b. Transpose the matrix which you defined as m in part 4
c. Transpose the matrix which you defined as p on part 4

7. Addition, Subtraction , Multiplication, and Division of Matrices :

a. Add 5 to the matrix that you defined as p
b. Which of the elements in matrix p increased by 5?
c. Multiply every element in matrix m by 2
d. Square every element in matrix p

Now let’s add two matrices together. To do this we must have two matrices that are
the same size. When adding matrices the corresponding elements add together.

e. Add together the matricesand

To divide matrices they also must be the same size. When dividing matrices
the corresponding elements are divided.

f. Divide matrix r by matrix t
To multiply matrices use the command (matrix 1).(matrix 2)
g. Multiply matrix m and matrix p (this is known as the dot product)
h. Multiply matrix r and matrix t
i. Multiply matrix p and matrix m
j.
8. Inverse Matrix: The inverse of a matrix can be found using the command Inverse[m]
where m is the matrix,

a. Find the inverse of matrix r
b. Find the inverse of matrix m What is wrong?

9. Determinant: To find the de terminant of a matrix use the command Det[m] where m
is the matrix
a. Find the determinant of matrix r
b. Find the determinant of matrix t
c. Find the determinant of the matrix

What is special about this matrix that gave you the determinant you got?

10. System of Equations : Using the Solve command you can have Mathematica
determine what variables must equal in systems of equations .
Find all of the variables in the following systems of equations

a.
 x + y + z = 4
x – 2y – z = 1
2x – y -2z = -1
b.
 x – y = 2
-2x + 2y = -4